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Abstract
A new circular distribution called Wrapped Log Kumaraswamy Distribution (WLKD) is introduced in this paper. We obtain explicit form for the probability density function and derive expressions for distribution function, characteristic function and trigonometric moments. Method of maximum likelihood estimation is used for estimation of parameters. The proposed model is also applied to a real data set on repair times and it is established that the WLKD is better than log Kumaraswamy distribution for modeling the data.
References:-
References
Adnan, M. A. S. and Roy, S. (2014). Wrapped variance gamma distribution with an application to wind direction. Journal of Environmental Statistics. 6(2):1-10.
Akinsete, A., Famoye, F. and Lee, C. (2014). The Kumaraswamy-geometric distribution.Journal of Statistical Distributions and applications. 1:17.
Alzaatreh, A., Lee, C. and Famoye, F.(2012). On the discrete analogues of continuous distributions. Stat. Meth. 9: 589-603.
Alzaatreh, A., Lee, C. and Famoye, F.(2013). A new method for generating families of continuous distributions. Metron. 71:63-79.
Artur J. Lemonte, Wagner Barreto-Souza and Gauss M. Cordeiro.(2013). The exponentiated Kumaraswamy distribution and its log-transform. Brazilian Journal of Probability and Statistics.Vol. 27. 1:31–53.
Batschelet, E. (1981). Circular Statistics in Biology. Academic Press, London.
Bourguignion, M., Silva M.B, Zea, L.M and Cordeiro, G.M. (2013). The Kumaraswamy Pareto distribution. J Stat Theor Appl. 12: 129-144.
Cordeiro, G.M. and de Castro, M. (2011). A new family of generalized distributions. J Stat Comput Simul. 81: 883-893.
Cordeiro, G.M., Ortega E.M.M. and Silva, G.O. (2014). The Kumaraswamy modified Weibull distribution: Theory and applications. J Stat Comput Simul. 84: 1387-1411.
Correa M.A., Nougueira D.A and Ferreira E.B. (2012). Kumaraswamy normal and Azzalini’s skew normal modeling asymmetry. Sigmae. 1: 65-83.
de Pascoa Mar, Ortega E.M.M.and Cordeiro, G.M. (2011). The Kumaraswamy generalized gamma distribution with application in survival analysis. Stat Methodol. 8: 411-433.
de Santana T.V.F., Ortega E.M.M., Cordeiro, G.M. and Silva, G.O. (2012). The Kumaraswamy log-logistic distribution. J Stat Theor Appl. 11: 265-291.
Eldin, M.M., Khalil,N. and Amein M.(2014). Estimation of parameters of the Kumaraswamy distribution based on general progressive type II censoring. American Journal of Theoretical and Applied Statistics. 3(6): 217-222.
El-Sherpieny E.S.A., and Ahmed M.A. (2011). On the Kumaraswamy-Gumbel distribution. Paper presented at 46th Ann Conf Statist Comput Sci Oper Res, ISSR-Cairo University, Egypt.
Elbatal, I. (2013a). Kumaraswamy linear exponential distribution. Pioneer J Theor Appl Statist. 5: 59-73.
Elbatal, I. (2013b). Kumaraswamy generalized linear failure rate distribution. Indian J Comput Appl Math. 1: 61-78.
Elbatal, I. (2013c). Kumaraswamy exponentiated Pareto distribution. Economic Quality Control. 28: 1-8.
Fang, K.T., Kotz,S. and Ng,K.W. (1990). Symmetric Multivariate and Related Distributions. Chapman and Hall, London.
Fletcher, S.C., and Ponnamblam, K. (1996). Estimation of reservoir yield and storage distribution using moments analysis. J Hydrol. 182:259–275.
Gomes, A.E., Da Silva, C.Q., Cordeiro, G.M.and Ortega E.M.M. (2014). A new lifetime model: The Kumaraswamy generalized Rayleigh distribution. J Stat Comput Simul. 84: 290-309. 21. Gupta, R.C. Kirmani, SNUA. (1988). Closure and monotonicity properties of nonhomogeneous Poisson processes and record values. Probab Eng Inf Sci. 2:475–484.
Huang,S. and Oluyede,B.O. (2014). Exponentiated Kumaraswamy-Dagum Distribution with Applications to Income and Lifetime Data. Journal of Stati. Distri. and Applications. 1:8.
Jacob, S. and Jayakumar K. (2013). Wrapped geometric distribution: A new probability model for circular data. Journal of Statistical Theory and Applications. 12(4):348-355.
Jammalamadaka S. Rao and SenGupta, A. (2001). Topics in Circular Statistics. New York, World Scientific.
Jammalamadaka S. Rao and Kozubowski, T. J. (2004). New families of wrapped distributions for modeling skew circular data. Communications in Statistics- Theory and Methods. 33(9):2059-2074.
Jammalamadaka S. Rao and Kozubowski, T. J. (2017). A General Approach for Obtaining Wrapped Circular Distributions via Mixtures. Sankhya : The Indian Journal of Statistics. 79:133-157.
Jorgensen, B. (1982). Statistical Properties of the Generalized Inverse Gaussian Distribution. New York: Springer-Verlag.
Joshi, S and Jose, K.K.(2017). Wrapped Lindley Distribution. Communications in Statistics- Theory and Methods.
doi/10.1080/03610926.201701280168(online version)
Kazemi, M.R., Haghbin, H. and Behboodian J.(2011). Another generalization of the skew normal distribution. World Appl Sci J. 12: 1034-1039.
Kumaraswamy P. (1976). Sine power probability density function. Journal of Hydrology. 31:181–184.
Kumaraswamy P. (1978). Extended sine power probability density function. Journal of Hydrology. 37:81–89.
Kumaraswamy, P. (1980). A generalized probability density function for double-bounded random processes. Journal of Hydrology. 46: 79–88.
Mardia, K. V. and Jupp, P. E. (2000). Directional Statistics. 2nd edition, New York, Wiley.
Muthulakshmi, S. and Selvi, B.G.G. (2013). Double sampling plan for truncated life test based on Kumaraswamy-log-logistic distribution. IOSR J Math. 7: 29-37.
Nadarajah, S., Cordeiro, G.M. and Ortega, E.M.M. (2012a). General results for the Kumaraswamy G distribution. J Stat Comput Simul. 87: 951-979.
Paranaiba, P.F., Ortega, E.M.M., Cordeiro, G.M. and Pascoa, M.A.R. (2013). The Kumaraswamy Burr XII distribution: Theory and practice. J Stat Comput Simul. 83: 2117-2143.
Ponnambalam, K., Seifi A., and Vlach, J. (2001). Probabilistic design of systems with general distributions of parameters. Int J Circuit Theory Appl. 29:527–536.
Rao, A.V. D., Sarma I.R., and Girija, S. V. S. (2007). On wrapped version of some life testing models. Communications in Statistics-Theory and Methods. 36:2027- 2035.
Rao, A.V.D., Sarma I.R., and Girija, S. V. S. (2013). On characteristics of wrapped gamma distribution. Engineering Science and Technology: An InternationaJournal. 3(2).
Roy, S. and Adnan, M. A. S. (2012). Wrapped weighted exponential distributions. Statistics and Probability Letters. 82:77-83.
Roy, S. and Adnan, M. A. S. (2012). Wrapped generalized Gompertz distribution: An application to Ornithology. Journal of Biometrics and Biostatistics. 3(6):
DOI 10.4172/2155-6180.1000153.
Saulo, H., Leao, J. and Bourguignion, M. (2012). The Kumaraswamy Birnbaum-Sanders distribution. J Stat Theory Pract. 6: 754-759.
Seifi A, Ponnambalam K, Vlach J (2000). Maximization of manufacturing yield of systems with arbitrary distributions of component values. Ann Oper Res. 99:373–383.
Shams, T.M. (2013). The Kumaraswamy- generalized Lomax distribution. Middle-East J Sci Res. 17: 641-646.
Shahbaz, M.Q., Shahbaz,S. and Butt N.S. (2012). The Kumaraswamy inverse-Weibull distribution. Pakistan J Statist Oper Res. 8: 479-489.
Sundar V.and Subbiah, K. (1989). Application of double bounded probability density function for analysis of ocean waves. Ocean Eng. 16:193–200.
Tahir, M.H. and Nadarajah, S. (2015). Parameter induction in continuous univariate distributions: Well-established G families. Anais da Academia Brasileira de Ciencias. http://dx.doi.org/10.1590/0001-3765201520140299
Zar, J.H. (1999). Biostatistical Analysis. 4th Edition, Prentice-Hall, Inc.